Abstract: A system for detecting and resolving conflicts between a plurality of aircraft or other objects on potentially conflicting trajectories in space. A two-dimensional graph generated on a processor-controlled display depicts the trajectory of one of the aircraft and creates particles that have identical velocity as the particular aircraft of interest. Each particle is at a different initial position from all other particles (in the sense of mathematical physics, a field is defined). That is, motion constraints are defined in terms of particles with specific characteristics and a algorithms for conflict avoidance are constructed by selecting a given particle which satisfies all of the constraints.